Duke Applied Mathematics

Publications [#243858] of Jonathan C. Mattingly

Papers Published

1. Mattingly, JC; Suidan, TM, The small scales of the stochastic Navier-Stokes equations under rough forcing, Journal of Statistical Physics, vol. 118 no. 1-2 (January, 2005), pp. 343-364, Springer Nature, ISSN 0022-4715 (ISSN: 0022-4715.) [MR2122959], [math-ph/0408060], [Gateway.cgi], [doi]
   (last updated on 2024/04/19)

   Abstract:
   We prove that the small scale structures of the stochastically forced Navier-Stokes equations approach those of the naturally associated Ornstein-Uhlenbeck process as the scales get smaller. Precisely, we prove that the rescaled kth spatial Fourier mode converges weakly on path space to an associated Ornstein-Uhlenbeck process as |k| → ∞. In addition, we prove that the Navier-Stokes equations and the naturally associated Ornstein-Uhlenbeck process induce equivalent transition densities if the viscosity is replaced with hyperviscosity. This gives a simple proof of unique ergodicity for the hyperviscous Navier-Stokes system. We show how different strengthened hyperviscosity produce varying levels of equivalence.